Exam 4: Solving Systems of Linear Equations

Fill in the blank with one of the words or phrases listed below. system of linear equations solution consistent independent dependent inconsistent substitution addition -In a system of linear equations in two variables, if the graphs of the equations are different, the equations are equations.

Solve the system of equations by either the addition method or the substitution method. - $\left\{ \begin{array} { l } \frac { x + 3 } { 4 } = \frac { y + 19 } { 8 } \\\frac { x } { 3 } = \frac { 2 y + 6 } { 6 }\end{array} \right.$

Is the ordered pair a solution of the linear system? - $\left\{ \begin{array} { l } 5 x - 5 y = 20 \\4 x + 4 y = - 4\end{array} ; ( 2 , - 2 ) \right.$

Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even. - C(x)=51x+2200 R(x)=71x

Fill in the blank with one of the words or phrases listed below. system of linear equations solution consistent independent dependent inconsistent substitution addition -Two algebraic methods for solving systems of equations are and .

Solve. -The sum of two numbers is $- 5$ . Three times the first number equals 4 times the second number. Find the two numbers.

Solve the system. -

Without graphing, decide: (a) Are the graphs of the equations are identical lines, parallel lines, or lines intersecting at a single point? (b) How many solutions does the system have? - $\left\{ \begin{array} { l } x + y = 7 \\x + y = 2\end{array} \right.$

Solve. -Kelly is a partner in an Internet-based seed and garden supply business. The company offers a blend of exotic wildflower seeds for $\$ 75$ per pound and a blend of common wildflower seeds for $\$ 30$ per pound. Kelly is creating a medium-price product by mixing together 31 pounds of the more expensive blend with 6 pounds of the less expensive blend. What will be the price per pound for the new blend? (Round to the nearest cent, if necessary.)

Solve the problem by writing and using a system of linear equations. -Two numbers have a sum of 119 and a difference of 55. Find the numbers.

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } x + y = 4 \\x - y = 4\end{array} \right.$

Solve. -Julie and Eric row their boat (at a constant speed) 60 miles downstream for 6 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 10 hours. Find the rate of the current.

Solve. -One number is 6 less than a second number. Twice the second number is 40 more than 4 times the first. Find the two numbers.

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } 4 x + y = 3 \\5 x - y = 6\end{array} \right.$

Solve the system by the substitution method or the addition method. - $\left\{ \begin{array} { l } 3 x + y = 5 \\4 x + 3 y = 0\end{array} \right.$

The double line graph below shows the number of Acme Superstores vs. the number of General Superstores. -In what year was the number of Acme stores approximately equal to the number of General stores?

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } 4 x - 3 y = - 23 \\y = x + 6\end{array} \right.$

Solve. -Jarod is having a problem with rabbits getting into his vegetable garden, so he decides to fence it in. The length of the garden is 4 feet more than 3 times the width. He needs 56 feet of fencing to do the job. Find the length and width of the garden.

Solve the system of equations by graphing. - $\left\{ \begin{aligned}2 x - y & = - 7 \\y & = 1\end{aligned} \right.$

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } 4 x - 6 y = 7 \\- 2 x + 3 y = 2\end{array} \right.$